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26 Apr 2019, 07:34
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A
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Difficulty:
15%
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Question Stats:
76% (00:57) correct
24%
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wrong
based on 929
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If three straight lines intersect at a point as shown in the figure above, what is the value of x ?
(1) x = y = z
(2) z = 60
DS03602.01
Quantitative Review 2020 NEW QUESTION
Attachment:
2019-04-26_1833.png [ 6.03 KiB | Viewed 13938 times ]
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26 Apr 2019, 12:36
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The Precise approach to this question will use the given information to find the specific numbers. We would rarely need to do this in DS questions, but this question provides a lot of information to start with: since two opposite angles between intersecting lines are equal, and since the sum of angles in a full circle is 360, we know that x+y+z+x+y+z=360, so 2x+2y+2z=360.
Statement (1): if x=y=z, then (using 2x+2y+2z=360) we get 2x+2x+2x=360 >>> 6x=360 >>> x=60. Since statement (1) is enough on its own, answer choices (B), (C) and (E) are eliminated.
Statement (2): If z=60, then (using 2x+2y+2z=360) we get 2x+2y+120=360. This is an equation with two variables, and thus not enough to find the exact value of x. Answer choice (D) is eliminated.
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Statement (1): if x=y=z, then (using 2x+2y+2z=360) we get 2x+2x+2x=360 >>> 6x=360 >>> x=60. Since statement (1) is enough on its own, answer choices (B), (C) and (E) are eliminated.
Statement (2): If z=60, then (using 2x+2y+2z=360) we get 2x+2y+120=360. This is an equation with two variables, and thus not enough to find the exact value of x. Answer choice (D) is eliminated.
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Updated on: 17 May 2021, 07:29
Originally posted by BrentGMATPrepNow on 24 Mar 2020, 08:34.
Last edited by BrentGMATPrepNow on 17 May 2021, 07:29, edited 1 time in total.
Last edited by BrentGMATPrepNow on 17 May 2021, 07:29, edited 1 time in total.
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Bunuel
Target question: What is the value of x ?
Since opposite angles are equal, we can add a few more things to our diagram to get:
Statement 1: x = y = z
Since angles on a line add to 180°, we can see that the along the blue line must add to 180°
So, x + y + z = 180
If all three angles are equal, then x = y = z = 60
The answer to the target question is x = 60
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: z = 60
Let's add this information to the diagram to get:
Notice that, if we rotate the green line, the value of x changes (for more on this strategy, see the second video below).
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
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